The former England international made his return in the Reds Under-21s' win over Fulham after being sidelined since August.
The 30-year-old scored in his hour-long appearance for the youth side and is now desperate to play his way into Brendan Rodgers's squad.
"It was nice to get out there and play and I felt okay fitness-wise," said Cole.
"It's always nice to score but I think the main thing for me was really to just get through the game and test myself to see how my fitness is and how my sharpness is.
"I was happy and it's a case of onwards and upwards now and hopefully I can be available for the first team. I think the manager will probably assess my fitness and we'll go from there. I need to get back in the first team. I want to be out there playing."
Cole spent last season on loan at Lille.